hdu 5625 Clarke and chemistry

Problem Description

Clarke is a patient with multiple personality disorder. One day, Clarke turned into a junior student and took a chemistry exam.  But he did not get full score in this exam. He checked his test paper and found a naive mistake, he was wrong with a simple chemical equation balancer.  He was unhappy and wanted to make a program to solve problems like this.  This chemical equation balancer follow the rules:  Two valences A combined by |A| elements and B combined by |B| elements.  We get a new valence C by a combination reaction and the stoichiometric coefficient of C is 1. Please calculate the stoichiometric coefficient a of A and b of B that aA+bB=C,  a,b∈N∗.

 

Input

The first line contains an integer T(1≤T≤10), the number of test cases.  For each test case, the first line contains three integers A,B,C(1≤A,B,C≤26), denotes |A|,|B|,|C| respectively.  Then A+B+C lines follow, each line looks like X c, denotes the number of element X of A,B,C respectively is c. (X is one of 26 capital letters, guarantee X of one valence only appear one time, 1≤c≤100)

 

Output

For each test case, if we can balance the equation, print a and b. If there are multiple answers, print the smallest one, a is smallest then b is smallest. Otherwise print NO.

 

Sample Input

2
2 3 5
A 2
B 2
C 3
D 3
E 3
A 4
B 4
C 9
D 9
E 9
2 2 2
A 4
B 4
A 3
B 3
A 9
B 9

 

Sample Output

2 3
NO

Hint:
The first test case, $a=2, b=3$ can make equation right.
The second test case, no any answer.

 

Source

BestCoder Round #72 (div.2)

 

 #pragma comment(linker, "/STACK:1024000000,1024000000")
 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<cmath>
 #include<math.h>
 #include<algorithm>
 #include<queue>
 #include<set>
 #include<bitset>
 #include<map>
 #include<vector>
 #include<stdlib.h>
 using namespace std;
 #define ll long long
 #define eps 1e-10
 #define MOD 1000000007
 #define N 1000000
 #define inf 1e12
 int a,b,c;
 int mp[][];
 int mpp[][];
 int vis[];
 int main()
 {
     int t;
     scanf("%d",&t);
     while(t--){
         memset(mpp,,sizeof(mpp));

         scanf("%d%d%d",&a,&b,&c);
         char s[];
         int cnt;
         for(int i=;i<a;i++){
             scanf("%s%d",s,&cnt);
             int index = s[]-'A';
             mpp[][index]+=cnt;
             //printf("1---%d\n",mp[0][index]);
         }
         for(int i=a;i<a+b;i++){
             scanf("%s%d",s,&cnt);
             int index = s[]-'A';
             mpp[][index]+=cnt;
             //printf("2---%d\n",mp[1][index]);
         }
         for(int i=a+b;i<a+b+c;i++){
             scanf("%s%d",s,&cnt);
             int index = s[]-'A';
             mpp[][index]+=cnt;
             //printf("3---%d\n",mp[2][index]);
         }

         int i,j;
         int flag=;
         for(i=;i<=;i++){
             for(j=;j<=;j++){
                 for(int k=;k<;k++){
                     mp[][k]=mpp[][k];
                     mp[][k]=mpp[][k];
                     mp[][k]=mpp[][k];
                 }
                 memset(vis,,sizeof(vis));
                 for(int k=;k<;k++){
                     mp[][k]*=i;
                     mp[][k]*=j;
                 }
                 int w=;
                 for(int k=;k<;k++){
                     if(mp[][k]){
                         if(mp[][k]+mp[][k] == mp[][k]){
                             vis[k]=;
                         }else{
                             w=;
                             break;
                         }
                     }
                 }

                 if(w==){
                     for(int k=;k<;k++){
                         if(vis[k]== && (mp[][k] || mp[][k] || mp[][k])){
                             w=;
                             break;
                         }
                     }
                 }
                 if(w==){
                     flag=;
                     break;
                 }
             }
             if(flag==) break;
         }
         if(flag==){
             printf("%d %d\n",i,j);
         }else{
             printf("NO\n");
         }
     }
     return ;
 }

 //A 6 2 12
 //B 6  3 18
 //C 12  5 60